Exam 8: Further Applications of Integration

Find the area of the surface obtained by rotating the circle about the line Select the correct Answer

The marginal cost function is defined to be the derivative of the cost function.If the marginal cost of manufacturing x units of a product is (measured in dollars per unit) and the fixed start-up cost is use the Total Change Theorem to find the cost of producing the first 5,000 units.

Select the correct Answer for each question. -A trough is filled with a liquid of density .The ends of the trough are equilateral triangles with sides m long and vertex at the bottom.Find the hydrostatic force on one end of the trough.

Select the correct Answer for each question. -The standard deviation for a random variable with probability density function f and mean µ is defined Find the standard deviation for an exponential density function with mean

Select the correct Answer: for each question. -Find the length of the curve.

Select the correct Answer: for each question. -A rectangular tank has width 3 ft, height 2 ft, and length 7 ft.It is filled with equal volumes of water and oil.The oil has a weight density of and floats on the water.Find the force exerted by the mixture on one end of the tank.(The weight density of water is )

Select the correct Answer: for each question. -Find the arc length of the graph from A to B.

A trough has vertical ends that are equilateral triangles with sides of length 7 ft.If the trough is filled with water to a depth of 4 ft, find the force exerted by the water on one end of the trough.Round to one decimal place.(The weight density of water is 62.4 lb/ft3.) Select the correct Answer

Find the centroid of the region bounded by the curves.

Select the correct Answer: for each question. -Suppose the average waiting time for a customer's call to beAnswered by a company representative (modeled by exponentially decreasing probability density functions) is minutes.Find the median waiting time.

Select the correct Answer: for each question. -You are given the shape of the vertical ends of a trough that is completely filled with water.Find the force exerted by the water on one end of the trough.(The weight density of water is

Select the correct Answer: for each question. -Dye dilution is a method of measuring cardiac output.If mg of dye is used and c(t) is the concentration of the dye at time then the cardiac output over the time interval is given by Find the cardiac output over the time interval [0, 15] if the dye dilution method is used with of dye and the dye concentration, in mg/L, is modeled by where is measured in seconds.

Find the area of the surface obtained by revolving the given curve about the x-axis.

Select the correct Answer: for each question. -Find the centroid of the region bounded by the graphs of the given equations.

Find the centroid of the region bounded by the graphs of the given equations.

Find the centroid of the region bounded by the given curves.

Find the length of the curve.

Select the correct Answer: for each question. -You are given the shape of the vertical ends of a trough that is completely filled with water.Find the force exerted by the water on one end of the trough.(The weight density of water is

The demand function for a commodity is given by Find the consumer surplus when the sales level is

Select the correct Answer: for each question. -Find the centroid of the region bounded by the given curves.